02.23.10 Modeling Exponential Functions.notebook
February 23, 2010
Answers to 10­3 Practice worksheet
OBJECTIVE
Students will be able to write an exponential function given two points.
Quick Review
x
y = a b
Form of an Exponential Function
The constant must always be a positive number.
If the exponential equation is y = ax, and a > 1, then the graph
of the function RISES as you move from left to right.
1) 1.544
2) 1.398
3) 0.146
4) -0.146
5) 2.389
6) 2.243
7) -0.699
8) 0.553
9) 4
10) 8
11) 6
12) 12
13) 2
14) 3
15) ¼
16) 4
17) 2
18) 1
19) 2
20) 0
21) 2
22) 3
23) 25
24) 4
25) 4
26) 3
27) 8
28) 0
29) 101
30) 6
Given two points write an exponential function of the form y = abx.
Step 1: Write as a system of equations.
Step 2: Solve one equation for a.
Step 3: Substitute into the other equation.
Step 4: Solve for b.
Step 5: Input value for b into equation solved for a.
The greater the value of a, the more quickly the graph will rise.
If the exponential equation is y = a-X, and a > 1, then the graph
of the function FALLS as you move from left to right.
Step 6: Write your Exponential Function.
The greater the value of a, the more quickly the graph will fall.
1
02.23.10 Modeling Exponential Functions.notebook
GIVEN: (1, 4) (2, 12)
1
4 = a b
12 = a b2
Step 1: Write as a system
of equations.
4 = a
b1
February 23, 2010
Step 5: Input value for b into equation
solved for a.
4 = a
3
y = 4 3x
3
Step 6: Write your Exponential Function.
Step 2: Solve one equation for a.
12 = 4 b2
b1
Step 3: Substitute into the other equation.
12 = 4 b1
3 = b
Step 4: Solve for b.
1
YOUR TURN!!!
CHANGE OF BASE FORMULA
GIVEN: (6, 8) (7, 32)
Log Answer
Log Given Base
Given two points write an exponential function of the form y = abx.
Use this if you want to find a value that isn't in Log10.
x
y = (1/512) 4
Ln Answer
Ln Given Base
HOW TO WRITE A POWER FUNCTION
Step 1: Write as a system of equations.
Step 2: Solve one equation for a.
Write a power function y = axb whose graph passes through
(1, 4) and (2, 12).
4 = a 1b
12 = a 2b
Step 1: Write as a system
of equations.
4 = a
1b
Step 2: Solve one equation for a.
Step 3: Substitute into the other equation.
Step 4: Solve for b.
Step 5: Write as a logarithm.
Step 6: Use change of base formula.
Step 7: Input value for b into equation solved for a.
Step 8: Write your POWER Function.
12 = 4 2b
1b
Step 3: Substitute into the other equation.
2
02.23.10 Modeling Exponential Functions.notebook
12 = 4 2b
Step 4: Solve for b.
3 = 2b
Log23 = b
Log 3 = b
Log 2
Step 5: Write as a logarithm.
Step 6: Use change of base formula.
February 23, 2010
Step 7: Input value for b into equation
solved for a.
4 = a
1b
4 = a
1
1.585
4 = a
Step 8: Write your POWER Function.
y = 4x1.585 y = axb 1.585 = b
YOUR TURN!!!
Write a power function y = axb whose graph passes through
(2, 5) and (6, 9).
y = 3.45x
0.535
HOMEWORK
Chapter 8 - Lesson 7
page 513
# 18 - 40 even
3